An Explicit Fourth-Order Runge–Kutta Method for Dynamic Force Identification

Abstract

This paper presents a new technique for input reconstruction based on the explicit fourth-order Runge–Kutta (RK4) method. First, the state-space representation of the dynamic system is discretized by the explicit RK4 method under the assumption of linear interpolation for the dynamic load, leading to a recurrence equation between the current state and the previous state. Then, the mapping from the sequences of input to output is established through the recursive operation of the system equation and observation equation. Finally, the stabilized force information is recovered using the Tikhonov regularization method. This approach makes use of the good stability and high precision of the RK4 method; in addition, the computational efficiency is enhanced by avoiding the computation of the inverse stiffness matrix. The proposed method is numerically illustrated and validated with various excitations on a simple four-story shear building and a more complicated 2D truss structure, along with a detailed parametric study. The simulation studies show that the external loads can be reconstructed with high efficiency and accuracy under a low noise environment.